Question

Hypothesis Testing Using Rejection Regions. In Exercises 19–26, (a) identify the claim and state H0 and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic t, (d) decide whether to reject or fail to reject the null hypothesis and (e) interpret the decision in the context of the original claim. Assume the population is normally distributed.

21. Credit Card Debt A credit reporting agency claims that the mean credit card debt by the state is greater than $5500 per person. You want to test this claim. You find that a random sample of 30 states has a mean credit card debt of $5594 per person and a standard deviation of $597 per person. At a = 0.05, can you support the claim?

Answer 1

Solution :

= 5500

=5594

S =597

n = 30

a ) This is the right tailed test .

The null and alternative hypothesis is ,

H0 :    = 5500

Ha : >5500

b )The critical t value =1.70

c ) Test statistic = t

= ( - ) / S / n

= (5594 -5500) / 597 / 30

= 0.862

Test statistic = t =0.862

d ) P-value =0.1979

= 0.05  

P-value >

0.1979 > 0.05

e ) Fail to eject the null hypothesis .

There is insufficient evidence to suggest that